Angle-Based Sensor Network Localization

This article studies angle-based sensor network localization (ASNL) in a plane, which is to determine locations of all sensors in a sensor network, given locations of partial sensors (called anchors) and angle measurements obtained in the local coordinate frame of each sensor. First, it is shown that a framework with a nondegenerate bilateration ordering must be angle fixable, implying that it can be uniquely determined by angles between edges up to translations, rotations, reflections, and uniform scaling. Then, ASNL is proved to have a unique solution if and only if the grounded framework is angle fixable and anchors are not all collinear. Subsequently, ASNL is solved in centralized and distributed settings, respectively. The centralized ASNL is formulated as a rank-constrained semidefinite program (SDP) in either a noise-free or a noisy scenario, with a decomposition approach proposed to deal with large-scale ASNL. The distributed protocol for ASNL is designed based on intersensor communications. Graphical conditions for equivalence of the formulated rank-constrained SDP and a linear SDP, decomposition of the SDP, as well as the effectiveness of the distributed protocol, are proposed, respectively. Finally, simulation examples demonstrate our theoretical results.